Implementation of Computational Contact Analysis in Geotechnical Engineering

Abstract

Analyses of mechanical interactions between soil and structural members in geotechnical engineering are long-standing challenges in the design of piles, foundations, retaining walls, and culverts. Due to the high nonlinearity of these problems, numerical solutions using finite element method (FEM) and finite differences are dominant in engineering practice. In this paper, a detailed procedure of FEM implementation is presented to solve 2D frictional interaction problems with finite sliding. This presentation starts from the geometrically exact theory to express the kinematics of contact, virtual work equation and linearization in the local convective coordinate system. Formulations of the contact tangent stiffness become straightforward and easy to understand. Tangential behavior is simulated by the regularized Coulomb friction law and constraints are enforced by the penalty approach. If linear finite elements are used, local smoothing is essential to improve convergence performance. Two applications in geotechnical engineering are presented to demonstrate the capabilities of this implementation.